For the function f(x)=x^2-2x+1,
(a)find f(1)
f(x) = x² - 2x + 1
Replace every x
with (1)
f((1)) = (1)² - 2(1) + 1
We don't need the double parentheses after the f, and we will
drop the color scheme:
f(1) = (1)² - 2(1) + 1
Now we simplify the right side:
f(1) = 1 - 2 + 1
f(1) = 0
(b) solve f(x)=0
f(x) = x² - 2x + 1
Put a zero where the f(x) is
0 = x² - 2x + 1
Swap sides:
x² - 2x + 1 = 0
Factor the left side:
(x - 1)(x - 1) = 0
Use the zero-factor principle:
x - 1 = 0 x - 1 = 0
x = 1 x = 1
Graph the function y=f(x)=x^2+1
Get some points:
x | y = f(x) = x² + 1 | point
-------------------------------------------------
-2 | y = f(-2) = (-2)² + 1 = 4 + 1 = 5 | (-2,5)
-1 | y = f(-1) = (-1)² + 1 = 1 + 1 = 2 | (-1,2)
0 | y = f(0) = (0)² + 1 = 0 + 1 = 1 | (0,1}
1 | y = f(1) = (1)² + 1 = 1 + 1 = 2 | (1,2)
2 | y = f(2) = (2)² + 1 = 4 + 1 = 5 | (2,5)
Plot those points:
Now draw a smooth U-shaped curve through those points:
Edwin
